Quantitative Finance For Dummies. Steve Bell
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a great insight when buying a call option and that share price shoots up, and you have to pay your client a large payoff. Ouch!
To mitigate the risk of selling options, you can and should delta hedge, which means to buy or sell the underlying asset associated with your option. Chapter 11 shows you how to calculate the value of delta for a plain vanilla equity option. If you don’t delta hedge and take a naked position, then you run the risk of large losses.
Building portfolios and reducing risk
Investment managers build large portfolios of shares, bonds and other financial assets. These portfolios are often part of pension funds or made available to private investors as mutual funds. How much of each asset should the manager buy for the portfolio? This decision depends on the manger’s objective but if, like many others, she wishes to maximise returns and reduce risk, she can use a framework called modern portfolio theory (MPT for short). MPT is not so modern now as it was first worked out by the economist Markowitz in 1952, but the framework and concepts are still applicable today. You can read about it in Chapter 14.
❯❯ The expected return of your assets
❯❯ The volatility of your assets
❯❯ The correlations (statistical relationships calculated from price returns) between your assets
From this, you can calculate the portfolio that meets your objectives. That may mean minimising the risk but it may also mean achieving some minimum level of return.
In practice, using MPT has proved difficult because both correlations and expected returns are hard to estimate reliably. But some timeless ideas do exist that were usefully highlighted by MPT. The main one is diversification, which has been described as the only free lunch in finance because of its almost universal benefits. By placing investments over a wide number of assets, you can significantly reduce the risk for the same level of return. Equivalently, you can boost your return for the same level of risk. By paying special attention to the correlation between the assets in your portfolio you gain maximum benefit from diversification. If the correlation between your assets is small or even negative, the benefit is large. Sadly that’s not easy to achieve because, for example, many stocks and shares are correlated, but at least you know what to look for. Chapter 14 talks more about tools to manage portfolios, including correlation and diversification.
Data can be gathered directly by monitoring activity on the Internet – especially trade data: the price, time and quantity of financial instruments bought and sold. The large amounts of data now captured means that more specialised databases are used to store it and more sophisticated machine learning techniques are used to model it. The better your models are, the more successfully you can trade, and the more data you generate for further analysis. A poet once wisely wrote that you can’t feed the hungry on statistics. You can’t eat data, but data is now a big industry employing – and feeding – many people. You may be one of them.
Seeing the signal in the noise
The problem with large amounts of data is what to do with it. The first thing is to plot it. Plotting allows you to spot any obvious relationships in the data. You can also see whether any data is missing or bad, which is an all-too-frequent occurrence.
❯❯ Line plot: A line plot or chart shows how a value Y (normally shown on the vertical axis) varies with a value indicated on the horizontal axis. The Y values are shown as a continuous line. A line plot is good for showing how a price or interest rate or other variable (Y) changes with time. You can overlay several line plots to compare the movement of several assets.
❯❯ Scatter plot: A plot of two variables, X and Y, against each other where each pair of values (X,Y) is drawn as a point. Scatter plots can look like a swarm of bees but are good for revealing relationships you may otherwise not spot. For example, you may want to plot the daily returns of a stock against the daily returns of a stock index to see how correlated they are.
❯❯ Histogram: Also known as a bar chart, a histogram is great for showing the distribution of the returns of a financial asset.
In Chapter 8 I show you how to investigate a bit deeper into histograms and discover a better representation of the returns distribution.
The Gaussian distribution is so frequently encountered in quantitative finance that you can easily forget that there are often more complex distributions behind your data. To investigate this, you can use the expectation maximisation algorithm, which is a powerful iterative way for fitting data to models. Go to Chapter 8 to find out more about this.
Keeping it simple
If you build models for the expected returns of an asset you’re trading or investing in, you need to take great care. If you apply a volatility adjustment to the returns of your asset, the returns look much like Gaussian random noise. Normally, Gaussian noise is what’s left after you build a model. So, because markets are nearly efficient, you have little to go on to build a model for returns. Also, you certainly can’t expect anything that has much predictive power.
Looking at the finer details of markets
In Chapter 18, you can find out more about markets in real life. Some of this information isn’t pretty, but it is important. One important mechanism is market impact, the amount by which prices move when you buy or sell an asset. In a way, this impact is the reason markets are important – prices change with supply and demand. The example using Bayes’ theorem shows how markets can take on new information and reflect it in changed prices. Doing so is the way that markets can become almost efficient.
Trading at higher frequency
More and more financial trading is completely automated. Computers running powerful algorithms buy and sell stocks and futures contracts often with holding periods of less than a second – sometimes less than a millisecond. This high frequency trading (HFT) must use maths and algorithms. It is part of quantitative finance and many quants are involved with the development of trading algorithms.
Chapter 2
Understanding Probability and Statistics
IN THIS CHAPTER
Comprehending that events can be random
Gathering data to produce statistics of random variables
Defining some important distributions
If you’ve ever placed a bet on a horse or wondered whether your date for the evening is going to turn up, then you know a bit about probability and statistics. The concepts get more interesting if you have multiple events or events in succession.
For example, if you manage to pick both the first and second place horses in a race (an exacta) does that mean you have real skill? This